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<h2 class="hd hd-2 unit-title">Topics and Reading List</h2>
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<p> As you go through the lesson, you will find this list of reading from the textbook complementary to the videos and exercises, and on many occasions these readings will contain relevant material to the presentation:</p><ul><li> Force Laws: <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/8/2"><i class="it">chapter 8, section 1</i></a></li><li> Constraint Forces: <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/8/9"><i class="it">chapter 8, section 3</i></a></li><li> Free Body Diagrams: <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/8/16"><i class="it">chapter 8, section 4</i></a></li></ul>
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<h2 class="hd hd-2 unit-title">L7v1: Pushing Pulling and Tension</h2>
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<h3 class="hd hd-2">L7v1: Pushing Pulling and Tension</h3>
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<h2 class="hd hd-2 unit-title">L7v2: Ideal Rope</h2>
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<p> Under what conditions can we say the tension is the same at any point of a rope?</p>
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<h3 class="hd hd-2">L7v2: Ideal Rope</h3>
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<h2 class="hd hd-2 unit-title">L7Q1: Block Accelerating Down</h2>
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L7Q1: Block Accelerating Down
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<p>
A 10-kg block is lowered by an attached string at a constant acceleration of 3 m/s[mathjaxinline]^2[/mathjaxinline] downwards. The string is massless. Use [mathjaxinline]g=9.8[/mathjaxinline] m/s[mathjaxinline]^2[/mathjaxinline] in your calculations. The magnitude of the force of tension in the string is </p>
<p>
<p style="display:inline">[mathjaxinline]T=[/mathjaxinline]</p>
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<h2 class="hd hd-2 unit-title">L7Q2: Two Hanging Boxes</h2>
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L7Q2: Two Hanging Boxes
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<p><b class="bfseries">(Part a)</b> Box A of mass [mathjaxinline]m_ A = 70[/mathjaxinline] kg and box B of mass [mathjaxinline]m_ B =[/mathjaxinline] 90 kg are hanging motionless from the ceiling. Ropes A and B are massless. What is [mathjaxinline]T_ A[/mathjaxinline], the magnitude of the force of tension in rope A? Use [mathjaxinline]g = 9.8[/mathjaxinline] m/s[mathjaxinline]^2[/mathjaxinline] in your calculations. </p>
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<p><b class="bfseries">(Part b)</b> If the lower rope, rope B, is cut, what is [mathjaxinline]T_ A[/mathjaxinline] the magnitude of the force of tension in the upper rope? Use [mathjaxinline]g = 9.8[/mathjaxinline] m/s[mathjaxinline]^2[/mathjaxinline] in your calculations. Neglect any possible oscillations resulting from cutting the rope. </p>
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<p><b class="bfseries">(Part c)</b> If the upper rope, rope A, is cut, what is [mathjaxinline]T_ B[/mathjaxinline], the magnitude of the force of tension in rope B? Use [mathjaxinline]g = 9.8[/mathjaxinline] m/s[mathjaxinline]^2[/mathjaxinline] in your calculations. Neglect any possible oscillations resulting from cutting the rope. </p>
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<h2 class="hd hd-2 unit-title">L7v3: Solving Pulley Systems</h2>
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<h2 class="hd hd-2 unit-title">L7Q3: Two Blocks and a Pulley</h2>
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Modified Atwood Machine: Block FBDs
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<p>Mass \(m_1\) is placed atop a frictionless table. A rope strung over a massless, frictionless pulley at the edge of the table connects mass \(m_1\) to a second mass \(m_2\) hanging over the table edge. </p>
<p>Draw a free-body diagram for masses \(m_1\) and \(m_2\). <em>Make sure that force vectors start with their tails near the appropriate object.</em></p>
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<h3 class="hd hd-3 problem-header" id="fbd2017_atwood_machine_modified_pulley-problem-title" aria-describedby="block-v1:MITx+8.01.1x+3T2018+type@problem+block@fbd2017_atwood_machine_modified_pulley-problem-progress" tabindex="-1">
Modified Atwood Machine: Pulley FBDs
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<p>Let's take a closer look at how the pulley changes the direction of tension forces in the rope.</p>
<p>Draw a free-body diagram a <strong>system</strong> consisting of the <strong>segment of rope in contact with the pulley</strong>.</p>
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<h2 class="hd hd-2 unit-title">L7Q4: Two Vertical Springs</h2>
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L7Q4: Two Vertical Springs
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<img src="/assets/courseware/v1/3457fbf01096a1b500939232c4b83a95/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_four_vertical_springs.svg" width="330"/>
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The two springs A and B depicted above are made of different materials and have different spring constants [mathjaxinline]k_ A[/mathjaxinline] and [mathjaxinline]k_ B[/mathjaxinline]. The springs happen to have the same natural length [mathjaxinline]L_0 = 0.1 \, \text {m}[/mathjaxinline]. </p>
<p>
An object of mass [mathjaxinline]m = 0.45 \, \text {kg}[/mathjaxinline] is hung from spring A, spring A is in equilibrium at a stretched length [mathjaxinline]L_ A = 0.24 \, \text {m}[/mathjaxinline]. When an identical object is hung from spring B, spring B settles down to an equilibrium stretched length [mathjaxinline]L_ B = 0.32 \, \text {m}[/mathjaxinline]. </p>
<p><b class="bfseries">(Part a)</b> What is the spring constant [mathjaxinline]k_ A[/mathjaxinline] of spring A, measured in N/m? <p style="display:inline">[mathjaxinline]k_ A=[/mathjaxinline]</p> <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ls_ls02_ls02_11_2_1" class=" capa_inputtype inline textline">
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<span class="trailing_text" id="trailing_text_ls_ls02_ls02_11_2_1">[mathjaxinline]\mathrm{(N/m)}[/mathjaxinline]</span>
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<p><b class="bfseries">(Part b)</b> What is the spring constant [mathjaxinline]k_ B[/mathjaxinline] of spring B, measured in N/m? <p style="display:inline">[mathjaxinline]k_ B=[/mathjaxinline]</p> <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ls_ls02_ls02_11_3_1" class=" capa_inputtype inline textline">
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<span class="trailing_text" id="trailing_text_ls_ls02_ls02_11_3_1">[mathjaxinline]\mathrm{(N/m)}[/mathjaxinline]</span>
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